Abstract
The discovery of the Higgs boson by the ATLAS and CMS collaborations allowed us to precisely determine its mass being 125.09±0.24 GeV. This value is intriguing as it lies at the frontier between the regions of stability and meta-stability of the standard model vacuum. It is known that the hierarchy problem can be interpreted in terms of the near criticality between the two phases. The coefficient of the Higgs bilinear in the scalar potential, m2, is pushed by quantum corrections away from zero, towards the extremes of the interval [−MPl2,MPl2] where MPl is the Planck mass. In this article, I show that demanding topological invariance for the renormalisation group allows us to extend the beta functions such that the particular value of the Higgs mass parameter observed in our universe regains naturalness. In holographic terms, invariance to changes of topology in the bulk is dual to a natural large hierarchy in the boundary quantum field theory. The demand of invariance to topology changes in the bulk appears to be strongly tied to the invariance of string theory to T-duality in the presence of H-fluxes.
Highlights
The discovery of the Higgs boson and the measurement of its mass as lying at the very edge between EW stability and metastability regions, not accompanied by the discovery of supersymmetric particles, already casts shadows of doubt upon a potential supersymmetric solution to the hierarchy problem
I show that naturalness can be restored if one imposes invariance of the physical theory with respect to topology changes associated to the renormalisation group
Having explained how the renormalisation group flows can be interpreted in geometric terms and, following [20], how the beta function can be interpreted as a geometric curvature, it remains to be seen how string theory can be formulated in a T-duality symmetric way so that we can transfer its topological invariance to low energy effective theories
Summary
The discovery of the Higgs boson by the ATLAS and CMS collaborations allowed us to precisely determine its mass being 125.09 ± 0.24GeV. This value is intriguing as it lies at the frontier between the regions of stability and meta-stability of the standard model vacuum. I show that demanding topological invariance for the renormalisation group allows us to extend the beta functions such that the particular value of the Higgs mass parameter observed in our universe regains naturalness. Invariance to changes of topology in the bulk is dual to a natural large hierarchy in the boundary quantum field theory. The demand of invariance to topology changes in the bulk appears to be strongly tied to the invariance of string theory to T-duality in the presence of H-fluxes
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